In December, about 20 people sipped Champagne at Lincoln Center’s David H. Koch Theater as members of New York City Ballet rehearsed the Nutcracker. The attendees toured backstage and chatted with the dancers before decamping to Bad Roman, a glitzy Italian restaurant in Columbus Circle, for dinner.

They were all guests of Mytheresa, an online luxury retailer that has two stores in Germany.

A new era of one-upmanship has taken hold in luxury shopping, where retailers and brands are vying to outdo each other to attract and retain wealthy shoppers. Mytheresa gets more than a third of its sales from just 3% of shoppers. At Neiman Marcus 2% of customers deliver 40% of sales. The brands are treating customers the way airlines treat frequent fliers and casinos treat “whales,” the highest rollers who get fancy suites, drinks and other amenities.

Gucci and Brunello Cucinelli are opening invitation-only boutiques in cities that include Los Angeles, Milan, Paris and New York, where shoppers can peruse the latest collections without brushing up against the masses.

Louis Vuitton and Burberry are targeting the uber wealthy with hotel-suite-worthy dressing rooms. Saks Fifth Avenue and Neiman Marcus are dialing up the perks with early access to exclusive collections and experiences that money alone can’t buy.

The efforts highlight a sobering reality for many sellers of luxury goods: After years of growth fueled by less-affluent shoppers shopping like affluent ones, luxury brands are watching their customer bases shrink and sales flag, particularly in the Americas, as more people feel the strain of high inflation and dwindling savings.

Many of these companies are responding by supercharging their courtship of the people who still have the means to spend.

Sales of personal luxury goods in the Americas fell 8% in 2023 to 101 billion euros, or about $110 billion, compared with 2022, according to Bain & Co. and Altagamma, the trade association for Italian luxury goods. Aspirational customers hit the brakes, while wealthier shoppers shifted their spending to other luxury segments such as travel and fine dining.

Sales are still growing at some companies, including LVMH Moët Hennessy Louis Vuitton and Mytheresa, but less than the turbocharged pace of recent years.

Neiman Marcus says it is focused on deepening relationships with those who spend more than $25,000 a year, because they are ultra loyal and more resilient to inflation and other market shocks.

“At my age, it’s harder to meet people—and the cool factor is hard to beat,” said Lisa Sher-Chambers, a 57-year-old stylist who lives in Manhattan and has made friends through these experiences. She posed for a photo at Mytheresa’s New York City Ballet event on stage with rows of empty seats behind her wearing a black Versace corset and Chanel skirt and posted it on Instagram. “I was blown away to be on that stage,” she said, adding that these types of experiences make her more inclined to purchase from Mytheresa in the future.

Companies say it is less expensive to get existing customers to spend more than to acquire new ones.

Online customer-acquisition costs have skyrocketed due to rising competition and new restrictions on the use of cookies, coding that helps marketers track people’s movements around the web. And digital marketing can’t create the pampering of physical experiences that people are craving.

The term VIP dates to at least the 1930s to denote people of importance. Companies have long catered to this group. Neiman Marcus’ InCircle rewards program, with perks that range from free gift wrapping to a concierge service that can arrange travel and event tickets, has been around since 1984. The events for top customers are separate from—and a cut above—the rewards program.

Lately some airlines have made it harder to acquire status, particularly for lower-tier customers, after looser rules during the Covid-19 pandemic gave too many people access to special perks. And while music festivals are suffering from lower revenue as fewer concertgoers buy general-admission passes, sales of VIP seats are booming.

“Everybody wants access,” said Heather Kaminetsky, Mytheresa’s North American president. “Clients will say, ‘How did you get us in? We’ve been trying to get a reservation for nine months.’”

Kim Dempster, a longtime Neiman Marcus shopper, lost the diamond from her engagement ring after celebrating her 30th anniversary last year. The retailerpaid for first-class airline tickets for her and her husband from their home in San Francisco to New York and put them up for three nights in December at the opulent Baccarat Hotel, decorated with the French company’s crystal, including 17 chandeliers and a display of 2,000 glasses at the entrance.

The couple had a private shopping appointment at the showroom of Bayco Jewels, one of Neiman Marcus’s suppliers, where they purchased a new diamond for her engagement ring and a yellow diamond for another ring—and dined at Cipriani’s with the jeweler’s founders.

Her husband Mark Dempster presented the new diamond set in her original engagement ring to her in the Bayco showroom by asking her to marry him for another 30 years.

“We get invited to loads of events,” said Mark, a venture capitalist. “Experiences like this are a different ballgame. Now, a set of memories have been created and relationships formed that you couldn’t do on your own.”

Dunja Grubjesa, a 37-year-old owner of a logistic company, said she is getting invited to more events lately, including a visit to the Valentino archives in Rome and a two-night stay in a castle in Sorrento, Italy, where the flower arrangements matched dinnerware from Aquazzura’s home collection—both hosted by Mytheresa.

Grubjesa, who divides her time between Miami and Chicago, said her husband jokes that despite the trips, she’s really not getting anything free. “He says I’ve already paid for everything they are giving me in purchases I’ve made,” she said.

Mytheresa, which recently hosted a lunch for clients at the home of Italian designers Domenico Dolce and Stefano Gabbana in Portofino, Italy, often allows guests to invite a plus-one. “This can unlock new customers for us,” said Kaminetsky.

Neiman Marcus hosted 50% more events for its best customers in 2023 compared with the previous year, including four days of red-carpet activities at the Cannes Film Festival. Guests were present at the unveiling of award statues created by Swiss jeweler and watchmaker Chopard; walked the red carpet and attended film premieres alongside celebrities and capped off the evening at after parties.

Neiman Marcus used to showcase fine jewelry in catalog mailings but took it up a notch in November when it hosted a black-tie ball at the Hôtel Swexan in Dallas. Guests spent the afternoon in private shopping appointments with six jewelers, including Boucheron and Chopard, who each had their own suites. In the evening, they descended to the ballroom for dinner and dancing. Nearly $140 million worth of jewelry was on display in an adjacent room so guests could continue browsing through the evening.

This year, Neiman Marcus is planning an all-expenses paid trip to Australia, where guests will visit the showroom of jewelry designer Margo McKinney and learn about pearl cultivation. Shoppers typically must spend upward of $10,000 a year to qualify for special treatment.

Saks recently expanded its Limitless VIP program to include more exclusive experiences, such as a partnership with Saint Laurent, where a portion of its more than 6,000 Limitless members were able to purchase certain items from the brand’s new collection 48 hours before they were available to the public. It recently hosted a weekend getaway to Aspen that included horse-drawn sleigh rides, skiing, spa treatments and private shopping appointments with a local jeweler.

“The aim for these events is to create long-lasting relationships with customers and to find people who will become ambassadors of the brand,” said Carolina Cucinelli, Brunello Cucinelli’s daughter and the brand’s co-president and co-creative director. The Italian brand, known for its quiet luxury aesthetic, has held events with Mytheresa and Neiman Marcus, where guests toured its private offices and were fitted for made-to-measure clothing.

“Customers really want that personal level of attention,” said Neiman Marcus President Ryan Ross.

Newly launched concierge-shopping service Long Story Short bills itself as a private club for power-shoppers and sells everything from Van Cleef & Arpels jewelry to Rolls-Royces. Clients pay a $1,000 monthly fee and undergo thorough vetting to get access. Hopeful members provide a driver’s license or passport, social-media links and complete a brief essay describing their background, upbringing or anything else that sheds light on what makes them unique.

Write to Suzanne Kapner at suzanne.kapner@wsj.com